Determine how many solutions exist for the system of equations. ${-18x-3y = 21}$ ${y = 1-6x}$
Solution: Convert both equations to slope-intercept form: ${-18x-3y = 21}$ $-18x{+18x} - 3y = 21{+18x}$ $-3y = 21+18x$ $y = -7-6x$ ${y = -6x-7}$ ${y = 1-6x}$ ${y = -6x+1}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -6x-7}$ ${y = -6x+1}$ Both equations have the same slope with different y-intercepts. This means the equations are parallel. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ Parallel lines never intersect, thus there are NO SOLUTIONS.